Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int INF = ~(1 << 31);
const double EPS = 1e-9;
const double PI = 3.141592653589793;
bool dfs(vector<vector<int> >& g, vector<bool>& u, int v) {
  u[v] = 1;
  for (int(i) = 0; (i) < (g[v].size()); (i)++) {
    int to = g[v][i];
    if (u[to])
      return 1;
    else if (dfs(g, u, to))
      return 1;
  }
  return 0;
}
int main() {
  vector<int> a;
  int k = 1;
  while (k * (k + 1) / 2 <= 1e9) {
    a.push_back(k * (k + 1) / 2);
    k++;
  }
  int n;
  cin >> n;
  for (int(i) = 0; (i) < (a.size()); (i)++) {
    for (int j = i; j < a.size(); j++) {
      if (a[i] + a[j] == n) {
        cout << "YES" << endl;
        return 0;
      }
    }
  }
  cout << "NO" << endl;
  return 0;
}